Beauville Surfaces and Groups / / edited by Ingrid Bauer, Shelly Garion, Alina Vdovina

• Record Nr.: UNINA9910299765003321
• Pubbl/distr/stampa: Cham : , : Springer International Publishing : , : Imprint : Springer, , 2015
• ISBN: 3-319-13862-6
• Edizione: [1st ed. 2015.]
• Descrizione fisica: 1 online resource (190 p.)
• Collana: Springer Proceedings in Mathematics & Statistics, , 2194-1009 ; ; 123
• Disciplina: 516.3/52; 516.35
• Soggetti: Algebraic geometry; Group theory; Number theory; Algebraic Geometry; Group Theory and Generalizations; Number Theory
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references.
• Nota di contenuto: Contents; Introduction; The Fundamental Group and Torsion Group of Beauville Surfaces; 1 Introduction; 2 Product-Quotient Surfaces; 3 The Fundamental Group; 4 Some Applications; References; Regular Algebraic Surfaces, Ramification Structures and Projective Planes; 1 Introduction; 2 Ramification Structures and Associated Surfaces; 2.1 Group Theoretical Structures; 2.2 From Ramification Structures to Algebraic Surfaces; 3 Groups with Special Presentations; 3.1 Ramification Structures for the Group in [15, Example 6.3]; 3.2 Ramification Structures for the Groups in [11, Example 3.3]; 3.3 Ramification Structures for the Group in [15, Example 6.4]3.4 Ramification Structures for the Groups of Theorem 3.1 with qge4; 3.5 Ramification Structures for the Group in [18, Example 2]; References; A Survey of Beauville p-Groups; 1 Introduction; 2 Definitions; 2.1 Beauville Structures; 2.2 p-Groups; 3 Beauville Groups in O'Brien Trees; 3.1 An Example; 3.2 Infinite Paths Through the O'Brien Trees; 4 Beauville Groups of Small Order; References; Strongly Real Beauville ; Groups; 1 Introduction; 2 The Finite Simple Groups; 3 Characteristically Simple Groups; 4 The Symmetric and Alternating Groups5 Almost Simple Groups; 6 Nilpotent Groups; References; Beauville Surfaces and Probabilistic Group Theory; 1 Beauville Surfaces and Beauville Structures; 2 Beauville Surfaces and Finite Simple Groups; 3 Hyperbolic Triangle Groups and Their Finite Quotients; 4 Beauville Structures for the Group `39`42`""613A``45`47`""603APSL2(q); 4.1 Sketch of the Proof of Theorem 10; 4.2 Proof of Theorem 7; 5 Beauville Structures for Finite Simple Groups; 5.1 Choosing Disjoint Conjugacy Classes; 5.2 Frobenius Formula and Witten's Zeta Function; 5.3 Character Estimates in Finite Simple Groups5.4 Finding Generating Pairs; References; The Classification of Regular Surfaces Isogenous to a Product of Curves with χ(mathcalOS)= 2; 1 Introduction; 2 Surfaces Isogenous to a Product; 3 Group Theory, Riemann Surfaces and Combinatorics; 4 Moduli Spaces; 5 The Algorithm and the Classification Result; 5.1 Exceptional Cases for Mainloop1:; 5.2 Exceptional Cases for Mainloop2:; References; Characteristically Simple Beauville Groups, II: Low Rank and Sporadic Groups; 1 Introduction; 2 Background and Method of Proof; 3 Generating Cartesian Powers; 4 Beauville Structures in Cartesian Powers5 The Groups L2(q); 6 Counting Triples; 7 The Suzuki Groups; 8 The Small Ree Groups; 9 The Sporadic Simple Groups; 9.1 The Mathieu Groups; 9.2 Other Small Sporadic Simple Groups; 9.3 The Larger Sporadic Simple Groups; 10 The Groups L3(q) and U3(q); 10.1 L3(q); 10.2 U3(q); References; Remarks on Lifting Beauville Structures of Quasisimple Groups ; 1 Introduction; 2 Frattini Covers of Beauville Groups; 3 Semidirect Products with Beauville Structures; 4 Questions; References; Surfaces Isogenous to a Product of Curves, Braid Groups and Mapping Class Groups
• Sommario/riassunto: This collection of surveys and research articles explores a fascinating class of varieties: Beauville surfaces. It is the first time that these objects are discussed from the points of view of algebraic geometry as well as group theory. The book also includes various open problems and conjectures related to these surfaces. Beauville surfaces are a class of rigid regular surfaces of general type, which can be described in a purely algebraic combinatoric way. They play an important role in different fields of mathematics like algebraic geometry, group theory and number theory. The notion of Beauville surface was introduced by Fabrizio Catanese in 2000 and, after the first systematic study of these surfaces by Ingrid Bauer, Fabrizio Catanese and Fritz Grunewald, there has been an increasing interest in the subject. These proceedings reflect the topics of the lectures presented during the workshop ‘Beauville Surfaces and Groups 2012’, held at Newcastle University, UK in June 2012. This conference brought together, for the first time, experts of different fields of mathematics interested in Beauville surfaces.